Department of Mathematical Sciences, Montclair State University, 1 Normal Avenue, Montclair, NJ 07043, USA.
Bull Math Biol. 2013 Sep;75(9):1450-71. doi: 10.1007/s11538-013-9855-0. Epub 2013 Jun 1.
We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model with a contact rate that fluctuates seasonally. Through the use of a nonlinear, stochastic projection, we are able to analytically determine the lower dimensional manifold on which the deterministic and stochastic dynamics correctly interact. Our method produces a low dimensional stochastic model that captures the same timing of disease outbreak and the same amplitude and phase of recurrent behavior seen in the high dimensional model. Given seasonal epidemic data consisting of the number of infectious individuals, our method enables a data-based model prediction of the number of unobserved exposed individuals over very long times.
我们考虑了一个带有季节性波动接触率的随机易感-暴露-感染-恢复（SEIR）传染病模型。通过使用非线性随机投影，我们能够分析确定确定论和随机动力学正确相互作用的低维流形。我们的方法产生了一个低维随机模型，它可以捕捉到高维模型中爆发疾病的相同时间以及反复发作行为的相同幅度和相位。给定由感染个体数量组成的季节性流行数据，我们的方法可以基于数据的模型预测在很长时间内未观察到的暴露个体数量。
